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Hedging Interest Rate Risk. Treasury/Eurodollar Futures. Derivative Securities. Stocks and Bonds represent claims to specific future cash flows Derivative securities on the other hand represent contracts that designate future transactions

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Hedging interest rate risk

Hedging Interest Rate Risk

Treasury/Eurodollar Futures


Derivative securities
Derivative Securities

  • Stocks and Bonds represent claims to specific future cash flows

  • Derivative securities on the other hand represent contracts that designate future transactions

  • Currently, there are approximately 300 million derivative contracts outstanding with a market value of around $50 Trillion

  • While equity trading is centered in New York (NYSE, NASDAQ), derivative markets are centered in Chicago (CME, CBOT, CBOE)


Futures contracts
Futures Contracts

A futures contract describes a transaction (Commodity, Price, and Quantity) that will be made in the future.

In “Trading Places” (1983), Eddie Murphy and Dan Ackroyd were trading Orange Juice Futures


Futures contracts1
Futures Contracts

Orange Juice futures (FCOJ) are traded on the NYBOT (New York Board of Trade)

Contract = 15,000 Lbs. ; Price = cents/lb

Every contract must have two participants (Long = Buy, Short = Sell)


Alongposition in MAR FCOJ would require you to purchase FCOJ in March

A short position in JUL FCOJ would require you to deliver FCOJ in March

Now

Mar

Apr

May

June

July

Aug


Dealers pass orders along to the pit traders who create a contract.

Long

Short

3 May Contracts (15k * 3 = 45k lbs.) @ 88 cents/lb.


The contracts are then passed along to the exchange who will become the middleman

Note: the exchange is holding two contracts with a zero net position

Short (3 contracts)

Long (3 contracts)

Long (3 Contracts)

Short (3 Contracts)


Contract completion fcoj
Contract Completion (FCOJ) become the middleman

First Notice Date

Last Delivery Date

Last Trading Day

First Delivery Date

Last Notice Date

May 1

May 8

May 10

May 23

May 31


Contract completion
Contract Completion become the middleman

Suppose that, on May 3, the short position decides that he wants out of the contract. The current May futures price is .92 per Lb

He could take a long position on 3 May contracts at a price of .92/LB

3 Contracts (Short) @ .88/LB

This would effectively “cancel out” the previous position at a loss of 3 cents/LB

.03*45,000 = $1,350 Loss

May 1

May 8

May 10

May 23

May 31


Contract completion1
Contract Completion become the middleman

Suppose that, on May 12, the short position opts for delivery of the commodity. The current spot price is .84 per Lb

3 Contracts (Short) @ .88/LB

The Exchange Pairs up Longs with Shorts

3 Contracts (Long) @ .88/LB

Profit = (.88-.84)*45,000

= $1,800

Loss = (.88-.84)*45,000

= $1,800

May 1

May 8

May 10

May 23

May 31


Types of futures
Types of Futures become the middleman


Stock index futures
Stock Index Futures become the middleman

  • Stock Index Futures have no underlying commodity

    • S&P 500

    • NYSE Composite

    • Value Line Index

These contracts are settled on a cash basis:Short Position Profits = (F – S)*500

Long Position Profits = (S – F)*500

F = Futures Price, S = Current Spot Price


Profits from price increases

Long Position

Short Position

Profits from price decreases


Treasury futures
Treasury Futures price of the underlying commodity.

Treasury futures first began trading on the CME in 1976. The underlying commodity is a Treasury Bill, Note, or Bond. Remember, when interest rates rise, Treasury prices fall!

Profits from price increases

Profits from decreasing interest rates

Long Position

Profits from price decreases

Profits from increasing interest rates

Short Position


T bill futures
T-Bill Futures price of the underlying commodity.

With T-Bill Futures, the commodity is a $1M Treasury Bill with 3 months left until maturity

Contracts exist for February, March, April, June, September, and December delivery

Last Trading Day (T-Bill Auction)

First Trading Day

Delivery Day

Nov 16, 2004

Feb 14

Feb 18


T bill yields
T-Bill Yields price of the underlying commodity.

We have already calculated the Yield to Maturity for 90 Day Treasury Bills

Face Value - Price

365

YTM =

*100

Price

t

Days left until maturity

Annualized

Often, the yield referred to for Treasury Bills is the discount yield

Annualized with a 360 day year

Face Value - Price

360

DY =

*100

Face Value

t

Interest As a percentage of Face Value rather than Price


Pricing t bill futures
Pricing T-Bill Futures price of the underlying commodity.

T-Bill futures are listed using the IMM (International Monetary Market) Index

IMM = 100 – Discount Yield

For example, if the Price of a $100, 90 Day Treasury were $98.

$100 - $98

360

DY =

*100 = 8%

$100

90

IMM = 100 – 8 = 92

Every .005 increase in the IMM raises the value of a long T-Bill position by $12.50 ($25 per basis point).


Eurodollar
Eurodollar price of the underlying commodity.

  • The term Eurodollar refers to deposits denominated in a currency other than the bank’s home currency

    • European banks offer Eurodollar time deposits (terms can range from overnight to several years)

    • European banks will lend dollar reserves to each other at the LIBOR rate (London Inter-bank Offering Rate)


Eurodollar futures 1981
Eurodollar Futures (1981) price of the underlying commodity.

  • The underlying commodity is a $1M 3 month Eurodollar time deposit. However, these deposits are not marketable. Therefore, Eurodollar futures are settled on a cash basis

  • Eurodollar futures can be treated like a T-Bill Future

IMM = 100 – LIBOR

Every .005 increase in the IMM raises the value of the long position by $12.50. ($25 per basis point)


Eurodollar futures vs t bill futures
Eurodollar Futures vs. T-Bill Futures price of the underlying commodity.

  • As the Eurodollar market grew, it became more liquid relative to the T-Bill market

  • LIBOR is a “risky” rate. Therefore, it correlates better with other risks


Pricing t bill eurodollar futures
Pricing T-Bill/Eurodollar Futures price of the underlying commodity.

Suppose that a march Eurodollar future (expires in 47 days) was currently selling for 94.555

We also have the current money rates (LIBOR)

IMM = 100 - LIBOR

This contract is paying an annualized (yield) of 100 – 94.555 = 5.445%


The Eurodollar Future currently has an annual yield of 5.445%

5.445

= 1.3613%

4

$1M (1.013613) = $1,013,613

Delivery of a $1M 90Day Eurodollar account

Purchase/Sale of Eurodollar Future

Receipt of $1,013,613

Now

Day 47

Day 137

90 Days


Use a linear interpolation to get the 47 day spot rate 5.445%

47

5.2175%

= .6811%

360

47 Day Return

Yield

5.3125%

5.2175%

5.18%

Term

1 Month

3 Months

47 Days


Use a linear interpolation to get the 137 day spot rate 5.445%

137

5.4855%

= 2.0875%

360

137 Day Return

Yield

5.6438%

5.4855%

5.3125%

Term

3 Months

6 Months

137 Days


The Eurodollar Future currently has an annual yield of 5.445%

5.445

= 1.3613%

4

S(47) = .6811%

S(137) = 2.0875%

Now

Day 47

Day 137

1.020875

=1.01397 = 1.3970% =

F(47,90)

1.006811


The Eurodollar Future currently has an annual yield of 5.445% (1.3613%)

IMM = 100 – 5.445 = 94.555

The implied no-arbitrage interest rate between 47 and 137 days is 5.588% (1.3970%)

IMM = 100 – 5.588 = 94.412

The interest rate on the futures contract is to low!!

or, alternatively

The price of the futures contract is too high!!!

Borrow at Futures Rate (Sell a Futures contract)

Now

Day 47

Day 137

Profit =

1.013970 – 1.013613

$1M = $357

Lend at the implied forward rate


How do you lend at the implied forward rate? 5.445%

By lending for the entire 137 day period and borrowing for the first 47 days, your net position is as a lender for the last 90 day period!

Borrow

Lend

Now

Day 47

Day 137


Go Short on a the futures contract at a price of 94.555 5.445%

Lend $992,885 for 137 days at the spot rate of 5.4855% (You will be paid $1,013,613 in 137 days)

Borrow $992,885 for 47 days at the spot rate of 5.2175%

Receive $1,013,613 from the original 137 day loan

Pay $1,013,613 on the 90 day loan

Borrow $1,000,000 at the rate established by the futures contract (5.445%)

Pay back the $992,885 Loan + interest ($999,643)

Now

Day 47

Day 137


On the 47 5.445%th day, you get a net cash flow of $352. This is the present value of $357 dollars to be received in 90 Days (you get the profits on day 47 rather than day 137)


The no arbitrage price of a price of a futures contract will reflect the forward rate implied by the yield curve. But remember, the forward rate is the expected future spot rate

Futures Rate = Expected Future Spot Rate


Treasury note bond futures
Treasury Note/Bond Futures reflect the forward rate implied by the yield curve. But remember, the forward rate is the expected future spot rate


The commodity for T-Note/Bond futures is a Treasury with a 6% annual coupon. What if there are no 6% bonds available?

Treasury Note/Bond futures are based on cheapest to deliver (CTD)basis.

  • Requirements for Delivery

  • The Face value of the delivered notes must sum to $100,000 (per contract)

  • All the notes must have the same characteristics (term, coupon)

It’s the short position’s option to deliver whatever has the lowest cost


Conversion factors
Conversion Factors 6% annual coupon. What if there are no 6% bonds available?

Suppose that you have a short position on a a Treasury bond future that expires this month (any bond with an expiration date between 2020 and 2030 would be acceptable for delivery:

The cheapest to deliver bond will always be the lowest coupon, longest maturity bond


Conversion factors1
Conversion Factors 6% annual coupon. What if there are no 6% bonds available?

The conversion factors are meant to make all deliverable bonds “equally attractive”

Invoice Amount

Contract Size

Futures Price

Conversion Factor

Accrued Interest

=


  • Requirements for Delivery 6% annual coupon. What if there are no 6% bonds available?

  • The Face value of the delivered notes must sum to $100,000 (per contract)

  • All the notes must have the same characteristics (term, coupon)

It’s the short position’s option to deliver whatever has the lowest cost

To Find the cheapest to deliver bond/note

Current Futures Price

Conversion Factor

Spot Price

Maximize

-

Note: This will always be negative


Pricing t note bond futures
Pricing T-Note/Bond Futures 6% annual coupon. What if there are no 6% bonds available?

20 Year Treasury Delivered

20 Year Treasury Expires

Now

March

March 2025

The Logic behind pricing treasury note/bond futures is the same as with T-Bill futures. The price should reflect expectation of future spot rates. However, note that expectations of future spot rates are already incorporated in bond prices!

Expected Future Treasury Price

Futures Price =

+ (Carry Costs – Carry Return)

Arbitrage Costs


Hedging
Hedging 6% annual coupon. What if there are no 6% bonds available?

Lets return to the 5 year Treasury Note example. Interest rates are currently 5% and are expected to stay at 5% (the yield curve is flat). A 5 year treasury note with $500,000 of face value and a 5% annual coupon.

$25,000

$25,000

$25,000

$25,000

$525,000

P

+

+

+

+

=

= $500,000

2

3

4

5

(1.05)

(1.05)

(1.05)

(1.05)

(1.05)

We already calculated the Modified Duration for this bond

MD = 4.3

That is, a 100 basis point increase in the interest rate lowers this bond’s price by (.043)($500,000) = $21,500


Hedging with t bill futures
Hedging with T-Bill Futures 6% annual coupon. What if there are no 6% bonds available?

Profits from price decreases

Profits from increasing interest rates

Short Position (Futures)

If you are long in bonds, you are worried about rising interest rates (rising interest rates lower the value of your bond). Therefore, you could hedge this risk by holding short positions in T-Bill futures (Short positions make money when interest rates drop)


Hedging with t bill futures1
Hedging with T-Bill Futures 6% annual coupon. What if there are no 6% bonds available?

Profits from price decreases

Profits from increasing interest rates

Short Position (Futures)

A perfect hedge eliminates all your interest rate risk

Change in value of each contract

Change in value of bond position

Change in value of Value of Futures position

# of Futures Contracts

=

=

$2,500

$21,500

$21,500/$2,500 = 8.6 Contracts


Hedging with t bill futures2
Hedging with T-Bill Futures 6% annual coupon. What if there are no 6% bonds available?

Change in value of each contract

Change in value of bond position

Change in value of Value of Futures position

# of Futures Contracts

=

=

$2,500

$21,500

$21,500/$2,500 = 8.6 Contracts

Dollar Duration of Bonds

MD(B)

FV(B)

4.3

$500K

=

Hedge Ratio =

=

MD(F)

FV(F)

.25

$1M

Dollar Duration of Futures


One Problem….. 6% annual coupon. What if there are no 6% bonds available?

X 100

Here we have the 5 year Treasury key durations. Note that this bond’s price is most sensitive to the 5 Year spot rate. The future’s value is based on the 90 day treasury rate


Change in value of each contract 6% annual coupon. What if there are no 6% bonds available?

Change in value of bond position

Change in value of Value of Futures position

# of Futures Contracts

=

=

$2,500

$21,500

$21,500/$2,500 = 8.6 Contracts

We assumed that the 90 Day T-Bill rate and the 5 Year Rate were perfectly correlated. Suppose, instead, that we have

Change in 90 Day Treasury Rate

Change in 5 Year Rate

= (.5)

The hedge ratio drops to 4.3!


Hedging with t note bond futures
Hedging with T-Note/Bond Futures 6% annual coupon. What if there are no 6% bonds available?

  • The strategy would be the same. If you are worried about increasing interest rates, take a short position in futures contracts. The hedge ratio for T-Note/Bond futures depends on

    • Size of bond position relative to the size of a futures contract

    • Duration of your bond position relative to the duration of the underlying asset in the futures contract

    • Correlation between the interest rate affecting your bond portfolio and the interest rate influencing the futures price

    • Impact of interest rate on CTD bond


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